Q.Anita prepared a fixture based on the league competition. She distributed this fixture to the coaches of all the teams. When Khushi received this fixture, it was misprinted and showed only the matches of rounds three and four. According to the above statement, study the fixture given below. [Figure: fixture showing only Round III and Round IV] III Round: 5 v Bye ; 4 v 6 ; 3 v 7 ; 2 v 1 IV Round: 4 v Bye ; 3 v 5 ; 2 v 6 ; 1 v 7 Based on the above fixture and your previous knowledge answer the following questions :

Cyclic Tournament Scheduling

Think about a round-robin tournament — the kind where every team plays every other team exactly once. Now imagine you have to schedule all those matches across several days or weeks, with each team playing exactly one match per round. That's the core problem. Cyclic tournament scheduling is the method of arranging those matches in a repeating, predictable pattern so that the schedule is fair, balanced, and easy to generate.

The basic intuition comes from a simple observation: if you have an even number of teams, you can fix one team in place and rotate the others around it in a circle. Each rotation produces one round of matches. This is why it's called "cyclic" — the schedule cycles through all possible pairings by rotating the positions.

The Precise Meaning

In a cyclic tournament schedule, the matches are arranged in rounds. In each round, every team plays exactly once. The schedule is generated by a fixed rotation pattern, usually with one team held stationary (the "anchor") and the others moving around it. For an odd number of teams, a "bye" (a dummy team) is added to make the count even, and the team that would play the bye gets a rest that round.

The key properties are:

• Every team plays every other team exactly once
• Each round has the same number of matches (half the number of teams, rounded down)
• The schedule is deterministic — given the number of teams, you can generate it mechanically
• It is fair — no team gets an advantage from the order of matches

Why It Matters

This method is not just a mathematical curiosity. It is the standard way to schedule tournaments in sports leagues, chess tournaments, and even some corporate events. The cyclic pattern ensures that the schedule is balanced: no team has to play two matches in a row while another rests, and the spacing between matches against strong opponents is roughly equal for everyone.

A Concrete Example Without Numbers

Imagine you have six teams. You arrange them in a circle, with one team fixed at the center. In the first round, each team plays the team directly opposite it. Then you rotate all the teams (except the fixed one) one position clockwise. That gives you the second round. You keep rotating until every team has played every other team. The result is a schedule that is easy to produce, easy to verify, and fair to all participants.

Common Variations

There are two main ways to implement the cyclic method: …

Sports Event Functions

When a school or sports body decides to hold a tournament, the work does not happen by itself — it happens because five distinct kinds of management action are carried out, one after another and often together. The CBSE Physical Education syllabus names these as the five functions of management, and they apply just as directly to running a sports event as they do to running any organisation: Planning, Organising, Staffing, Directing, and Controlling.

Planning comes first. It is the intellectual groundwork — deciding what the event will be, why it is being held, and the course of action that will get you there. Management writers describe this in slightly different ways. Koontz and O'Donnell call it "an intellectual process, a conscious determination of a course of action, basing decisions on purpose, facts and considered estimates." McFarland describes it as the executive skill of anticipating, influencing, and controlling the direction of change. Peter Drucker frames it as a continuous process of making entrepreneurial decisions today, with organised feedback to check whether they are working.

Good planning for a sports event is guided by six objectives:

• Goal oriented — every decision serves a stated aim (e.g., a well-run inter-house athletics meet).
• Policy — broad guidelines are set so decisions stay consistent as the event unfolds.
• Economy — the plan uses time, money, and effort efficiently.
• Defining the course of action — the exact steps and sequence are laid out in advance.
• Rules and regulations — the framework of do's and don'ts is fixed before the event, not improvised during it.
• Strategy — the plan anticipates obstacles (bad weather, a withdrawn team, a shortage of officials) and has a response ready.

Organising turns the plan into a working structure — this is where the Technical, Logistics, Finance, and Marketing committees are formed and given their specific pre-event, during-event, and post-event responsibilities. …

Sports Event Functions

When a school or sports body decides to hold a tournament, the work does not happen by itself — it happens because five distinct kinds of management action are carried out, one after another and often together. The CBSE Physical Education syllabus names these as the five functions of management, and they apply just as directly to running a sports event as they do to running any organisation: Planning, Organising, Staffing, Directing, and Controlling.

Planning comes first. It is the intellectual groundwork — deciding what the event will be, why it is being held, and the course of action that will get you there. Management writers describe this in slightly different ways. Koontz and O'Donnell call it "an intellectual process, a conscious determination of a course of action, basing decisions on purpose, facts and considered estimates." McFarland describes it as the executive skill of anticipating, influencing, and controlling the direction of change. Peter Drucker frames it as a continuous process of making entrepreneurial decisions today, with organised feedback to check whether they are working.

Good planning for a sports event is guided by six objectives:

• Goal oriented — every decision serves a stated aim (e.g., a well-run inter-house athletics meet).
• Policy — broad guidelines are set so decisions stay consistent as the event unfolds.
• Economy — the plan uses time, money, and effort efficiently.
• Defining the course of action — the exact steps and sequence are laid out in advance.
• Rules and regulations — the framework of do's and don'ts is fixed before the event, not improvised during it.
• Strategy — the plan anticipates obstacles (bad weather, a withdrawn team, a shortage of officials) and has a response ready.

Organising turns the plan into a working structure — this is where the Technical, Logistics, Finance, and Marketing committees are formed and given their specific pre-event, during-event, and post-event responsibilities. …